Poincare duality complexes in dimension four

Details Poincare duality complexes in dimension four Poincare duality complexes in dimension four

2008-02-25

arxiv.org/abs/0802.3652v2

Mathematics

Algebraic Topology

27 pages, made changes concerning examples in the literature after recieving helpful comments

Scientific paper

We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of Poincare duality complexes of dimension 4. Generalizing Turaev's fundamental triples of Poincare duality complexes of dimension 3, we introduce fundamental triples for Poincare duality complexes of dimension n > 2 and show that two Poincare duality complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional manifolds.

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